Primes and Predation

May 20, 2013 — Leave a comment

A shrill whine is engulfing the east coast of the United States. Millions of bluish-black cicadas, specifically Magicicada septendecim, will emerge per acre. These are not the Biblical locusts, more closely related to grasshoppers, but have been likened to them. When Brood II emerges and dies off a few weeks later, we can rest assured that the next emergence will not be until 2030. Magicicada, or periodical cicadas, operate on a 13- or 17-year cycle. Nearly the entire lifespan of each cicada is spent underground as a juvenile before the 4-6 week emergence as an adult, usually at high densities (over 300 per meter squared).

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Why do cicadas emerge en masse? The behavior is linked to an adaptation known as predator satiation. In other words, the high population density of cicadas ensures a low probability of being eaten by a predator. Birds, a main predator of cicadas, can only feast on so many until satiated, allowing the cicadas free reign for the first week or so of adulthood. Oak trees display a similar behavior through masting. Masting, in a general sense, refers to the production of fruits by trees. In some cases, a mass eruption of masts occurs after a long quiescent period. Oak trees, whose fruits are feed for animals, do so in what is called a mast year, where an abundance of such fruit is produced. Since this provides food for rodents, that “predator” is satiated. However, the populations of such rodents rise during mast years. Nonetheless, oak trees are able to generate enough fruit to reproduce, due simply to the mass production of said fruit.

As mentioned before, though, cicadas operate on 13- or 17-year cycles. Why does this matter? To answer this question, let’s talk about snowshoe hares. These hares operate on a 10-year population cycle. The rise and fall of snowshoe hare population coincided with a slightly out-of-phase rise and fall of Canadian lynx populations. These predator-prey dynamics were striking, and these apply to many species. The key point here is that the population cycles of predators and their prey may coincide for the snowshoe hare. Any predator with a one, two, five, or ten year cycle could align perfectly with the hare, as it does for the lynx. (This was recently featured in the New Yorker.)

Cicadas, however, operate a little differently. Their 13- and 17-year cycles are prime numbers. Since their cycles are only divisible by the cycle’s length (13 or 17) and one, it becomes difficult for predators to align their population cycles with the cicada. A predator with, let’s say, a three-year cycle should only align with the 17-year brood every 51 years (Note that many predators have 2-5 year life cycles.). Additionally, broods of different cycle lengths can rest assured that they will not overlap and thus compete for resources. This should only occur every 221 years, which I would argue is a rare brood overlap. Thus, there are two benefits for the use of prime numbers in cicada population cycles. First, predator population cycles are unlikely to align with large prime numbers. Second, different broods will rarely overlap.

In preparation for Brood II, I provide a recording from Brood X in 2004 of cicada calls. It is both enchanting and annoying. Please enjoy.

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